TSTP Solution File: SEV146^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV146^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:12:08 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 127 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 1010 ( 101 equ; 0 cnn)
% Maximal formula atoms : 3 ( 9 avg)
% Number of connectives : 2952 ( 121 ~; 111 |; 245 &;1726 @)
% ( 4 <=>; 350 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 182 ( 182 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 17 con; 0-2 aty)
% ( 395 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 492 ( 413 ^ 78 !; 0 ?; 492 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_17,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
sK2: a > a > $o ).
thf(func_def_19,type,
sK3: a ).
thf(func_def_20,type,
sK4: a ).
thf(func_def_21,type,
sK5: a ).
thf(func_def_22,type,
sK6: a > $o ).
thf(func_def_23,type,
sK7: a ).
thf(func_def_24,type,
sK8: a ).
thf(func_def_25,type,
sK9: a ).
thf(func_def_26,type,
sK10: a ).
thf(func_def_27,type,
sK11: a ).
thf(func_def_28,type,
sK12: a ).
thf(func_def_29,type,
sK13: a ).
thf(func_def_30,type,
sK14: a > $o ).
thf(f301,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f122,f176,f260,f300]) ).
thf(f300,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f299]) ).
thf(f299,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f298]) ).
thf(f298,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f292,f282]) ).
thf(f282,plain,
( ( ( sK14 @ sK12 )
= $false )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f281]) ).
thf(f281,plain,
( ( ( $true
=> ( sK14 @ sK12 ) )
= $false )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f278,f280]) ).
thf(f280,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK14 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f278]) ).
thf(f278,plain,
( ( ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK14 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK14 @ Y0 ) ) ) )
=> ( sK14 @ sK12 ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f277]) ).
thf(f277,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) )
@ sK14 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f271]) ).
thf(f271,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) )
= $false )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f270]) ).
thf(f270,plain,
( ( $false
= ( ( sK2 @ sK13 @ sK12 )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y1 )
& ( sK2 @ Y1 @ Y2 ) )
=> ( Y0 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK13 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK12 ) ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f269]) ).
thf(f269,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ Y0 @ sK12 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK12 ) ) ) )
@ sK13 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f268]) ).
thf(f268,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 @ sK12 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y2 )
& ( sK2 @ Y2 @ Y3 ) )
=> ( Y1 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK12 ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f267]) ).
thf(f267,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK12 ) )
| ~ spl0_1 ),
inference(sigma_clausification,[],[f15]) ).
thf(f15,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f14,plain,
( spl0_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f292,plain,
( ( ( sK14 @ sK12 )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f291]) ).
thf(f291,plain,
( ( $true
= ( $true
=> ( sK14 @ sK12 ) ) )
| ~ spl0_1 ),
inference(superposition,[],[f288,f272]) ).
thf(f272,plain,
( ( $true
= ( sK2 @ sK13 @ sK12 ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f270]) ).
thf(f288,plain,
( ! [X1: a] :
( ( ( sK2 @ sK13 @ X1 )
=> ( sK14 @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(beta_eta_normalization,[],[f287]) ).
thf(f287,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK14 @ Y0 ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_clausification,[],[f286]) ).
thf(f286,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK14 @ Y0 ) ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f285]) ).
thf(f285,plain,
( ( $true
= ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK13 @ Y0 )
=> ( sK14 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(backward_demodulation,[],[f280,f284]) ).
thf(f284,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK14 @ Y0 )
& ( sK2 @ Y0 @ Y1 ) )
=> ( sK14 @ Y1 ) ) ) )
= $true )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[],[f280]) ).
thf(f260,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f259]) ).
thf(f259,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f258]) ).
thf(f258,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f257,f212]) ).
thf(f212,plain,
( ( ( sK6 @ sK9 )
= $false )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f201]) ).
thf(f201,plain,
( ( $false
= ( ( ( sK2 @ sK10 @ sK9 )
& ( sK6 @ sK10 ) )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f200]) ).
thf(f200,plain,
( ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK9 ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f196]) ).
thf(f196,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> ( sK6 @ sK9 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f189]) ).
thf(f189,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) )
@ sK9 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f121]) ).
thf(f121,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f120,plain,
( spl0_4
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f257,plain,
( ( $true
= ( sK6 @ sK9 ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f256]) ).
thf(f256,plain,
( ( $true
= ( $true
=> ( sK6 @ sK9 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f255,f242]) ).
thf(f242,plain,
( ( $true
= ( sK6 @ sK11 ) )
| ~ spl0_4 ),
inference(binary_proxy_clausification,[],[f234]) ).
thf(f234,plain,
( ( ( ( sK2 @ sK11 @ sK9 )
& ( sK6 @ sK11 ) )
= $true )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f230,plain,
( ( ( ~ ( ( sK2 @ sK11 @ sK9 )
& ( sK6 @ sK11 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[],[f229]) ).
thf(f229,plain,
( ( ( ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
@ sK11 )
= $false )
| ~ spl0_4 ),
inference(sigma_clausification,[],[f217]) ).
thf(f217,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
~ ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f215]) ).
thf(f215,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK2 @ Y0 @ sK9 )
& ( sK6 @ Y0 ) )
=> $false ) )
= $false )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f196,f212]) ).
thf(f255,plain,
( ( $true
= ( ( sK6 @ sK11 )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f254]) ).
thf(f254,plain,
( ( $true
= ( ( ( sK6 @ sK11 )
& $true )
=> ( sK6 @ sK9 ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f112,f245]) ).
thf(f245,plain,
( ( $true
= ( sK2 @ sK11 @ sK9 ) )
| ~ spl0_4 ),
inference(boolean_simplification,[],[f244]) ).
thf(f244,plain,
( ( $true
= ( ( sK2 @ sK11 @ sK9 )
& $true ) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f234,f242]) ).
thf(f112,plain,
( ! [X2: a,X1: a] :
( $true
= ( ( ( sK6 @ X2 )
& ( sK2 @ X2 @ X1 ) )
=> ( sK6 @ X1 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f111]) ).
thf(f111,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ X1 ) )
@ X2 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f92]) ).
thf(f92,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK6 @ Y0 )
& ( sK2 @ Y0 @ X1 ) )
=> ( sK6 @ X1 ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f89]) ).
thf(f89,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f51]) ).
thf(f51,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f41]) ).
thf(f41,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f37]) ).
thf(f37,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f36]) ).
thf(f36,plain,
( ( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) )
@ sK6 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f28]) ).
thf(f28,plain,
( ( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f27]) ).
thf(f27,plain,
( ( ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK5 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK5 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f26]) ).
thf(f26,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) )
@ sK5 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f25]) ).
thf(f25,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f24]) ).
thf(f24,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 ) ) ) ) )
@ sK4 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f23]) ).
thf(f23,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK2 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y0 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y4 )
& ( sK2 @ Y4 @ Y3 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ sK3 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f22]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f18]) ).
thf(f18,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f17,plain,
( spl0_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) ) )
= $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f176,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f175]) ).
thf(f175,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f174,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f173,f130]) ).
thf(f130,plain,
( ( ( sK6 @ sK8 )
= $false )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f127]) ).
thf(f127,plain,
( ( ( ( sK2 @ sK7 @ sK8 )
=> ( sK6 @ sK8 ) )
= $false )
| ~ spl0_3 ),
inference(beta_eta_normalization,[],[f125]) ).
thf(f125,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK8 ) )
| ~ spl0_3 ),
inference(sigma_clausification,[],[f118]) ).
thf(f118,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f117,plain,
( spl0_3
<=> ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f173,plain,
( ( ( sK6 @ sK8 )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f172]) ).
thf(f172,plain,
( ( $true
= ( $true
=> ( sK6 @ sK8 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f159,f74]) ).
thf(f74,plain,
( ( $true
= ( sK6 @ sK7 ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f73]) ).
thf(f73,plain,
( ( $true
= ( $true
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f72,f51]) ).
thf(f72,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f71]) ).
thf(f71,plain,
( ( $true
= ( ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK6 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> ( sK6 @ sK7 ) ) )
| ~ spl0_2 ),
inference(superposition,[],[f66,f54]) ).
thf(f54,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $true )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f53]) ).
thf(f53,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f41,f51]) ).
thf(f66,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( X1 @ Y1 )
& ( sK2 @ Y1 @ Y0 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK7 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f65]) ).
thf(f65,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f47]) ).
thf(f47,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f44]) ).
thf(f44,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f39]) ).
thf(f39,plain,
( ( ( ~ ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( Y0 @ Y2 )
& ( sK2 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK7 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f38]) ).
thf(f38,plain,
( ( ( ^ [Y0: a] :
~ ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
@ sK7 )
= $false )
| ~ spl0_2 ),
inference(sigma_clausification,[],[f33]) ).
thf(f33,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
~ ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f31]) ).
thf(f31,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK2 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK2 @ sK4 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( Y1 @ Y3 )
& ( sK2 @ Y3 @ Y2 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> $false ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f25,f28]) ).
thf(f159,plain,
( ( ( ( sK6 @ sK7 )
=> ( sK6 @ sK8 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f154]) ).
thf(f154,plain,
( ( ( ( ( sK6 @ sK7 )
& $true )
=> ( sK6 @ sK8 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f112,f131]) ).
thf(f131,plain,
( ( ( sK2 @ sK7 @ sK8 )
= $true )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[],[f127]) ).
thf(f122,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f113,f17,f120,f117]) ).
thf(f113,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[],[f108]) ).
thf(f108,plain,
( ( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) )
| ~ spl0_2 ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f61,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f60]) ).
thf(f60,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( sK6 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( sK6 @ Y1 ) )
=> ( sK6 @ Y0 ) ) ) ) )
=> $false ) )
| ~ spl0_2 ),
inference(superposition,[],[f56,f43]) ).
thf(f43,plain,
( ( ( sK6 @ sK3 )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f42]) ).
thf(f42,plain,
( ( ( $true
=> ( sK6 @ sK3 ) )
= $false )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f37,f41]) ).
thf(f56,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ sK7 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK2 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) ) )
=> ( X1 @ sK3 ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[],[f55]) ).
thf(f55,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) )
@ X1 ) )
| ~ spl0_2 ),
inference(pi_clausification,[],[f50]) ).
thf(f50,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f49]) ).
thf(f49,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ sK7 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK2 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
& $true ) )
| ~ spl0_2 ),
inference(backward_demodulation,[],[f44,f47]) ).
thf(f19,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f17,f14]) ).
thf(f12,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[],[f11]) ).
thf(f11,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK2 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( Y2 @ Y3 )
& ( sK2 @ Y3 @ Y4 ) )
=> ( Y2 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK2 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK2 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK2 @ Y1 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y5 )
& ( sK2 @ Y5 @ Y4 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y0 ) ) ) ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[],[f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[],[f7]) ).
thf(f7,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f6]) ).
thf(f6,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y3 @ Y4 )
& ( Y0 @ Y4 @ Y5 ) )
=> ( Y3 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y2 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y4 @ Y6 )
& ( Y0 @ Y6 @ Y5 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X0 @ X5 @ X6 )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
& ! [X7: a] :
( ( X0 @ X2 @ X7 )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X1 ) )
& ! [X8: a > $o] :
( ( ! [X9: a,X10: a] :
( ( ( X8 @ X9 )
& ( X0 @ X9 @ X10 ) )
=> ( X8 @ X10 ) )
& ! [X11: a] :
( ( X0 @ X1 @ X11 )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X3 ) ) )
=> ! [X12: a > $o] :
( ( ! [X13: a,X14: a] :
( ( ( X0 @ X13 @ X14 )
& ( X12 @ X13 ) )
=> ( X12 @ X14 ) )
& ! [X15: a] :
( ( X0 @ X2 @ X15 )
=> ( X12 @ X15 ) ) )
=> ( X12 @ X3 ) ) )
& ! [X16: a,X17: a] :
( ( X0 @ X16 @ X17 )
=> ! [X18: a > $o] :
( ( ! [X19: a] :
( ( X0 @ X16 @ X19 )
=> ( X18 @ X19 ) )
& ! [X20: a,X21: a] :
( ( ( X0 @ X21 @ X20 )
& ( X18 @ X21 ) )
=> ( X18 @ X20 ) ) )
=> ( X18 @ X17 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ! [X2: a,X1: a,X6: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
=> ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ! [X2: a,X1: a,X6: a] :
( ( ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) )
& ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
=> ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X4: a,X5: a] :
( ( ( X0 @ X5 @ X4 )
& ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM525_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV146^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 19:06:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.36 % (4136)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.21/0.37 % (4132)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.21/0.37 % (4133)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.21/0.37 % (4132)Instruction limit reached!
% 0.21/0.37 % (4132)------------------------------
% 0.21/0.37 % (4132)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (4132)Termination reason: Unknown
% 0.21/0.37 % (4132)Termination phase: Saturation
% 0.21/0.37
% 0.21/0.37 % (4132)Memory used [KB]: 5500
% 0.21/0.37 % (4132)Time elapsed: 0.003 s
% 0.21/0.37 % (4132)Instructions burned: 5 (million)
% 0.21/0.37 % (4132)------------------------------
% 0.21/0.37 % (4132)------------------------------
% 0.21/0.37 % (4135)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.21/0.37 % (4137)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.21/0.37 % (4138)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.21/0.37 % (4134)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.21/0.37 % (4135)Instruction limit reached!
% 0.21/0.37 % (4135)------------------------------
% 0.21/0.37 % (4135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (4135)Termination reason: Unknown
% 0.21/0.37 % (4135)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (4135)Memory used [KB]: 1023
% 0.21/0.37 % (4135)Time elapsed: 0.003 s
% 0.21/0.37 % (4135)Instructions burned: 3 (million)
% 0.21/0.37 % (4135)------------------------------
% 0.21/0.37 % (4135)------------------------------
% 0.21/0.37 % (4131)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.21/0.37 % (4134)Instruction limit reached!
% 0.21/0.37 % (4134)------------------------------
% 0.21/0.37 % (4134)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (4134)Termination reason: Unknown
% 0.21/0.37 % (4134)Termination phase: Preprocessing 3
% 0.21/0.37
% 0.21/0.37 % (4134)Memory used [KB]: 1023
% 0.21/0.37 % (4134)Time elapsed: 0.003 s
% 0.21/0.37 % (4134)Instructions burned: 3 (million)
% 0.21/0.37 % (4134)------------------------------
% 0.21/0.37 % (4134)------------------------------
% 0.21/0.37 % (4138)Instruction limit reached!
% 0.21/0.37 % (4138)------------------------------
% 0.21/0.37 % (4138)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (4138)Termination reason: Unknown
% 0.21/0.37 % (4138)Termination phase: Saturation
% 0.21/0.37
% 0.21/0.37 % (4138)Memory used [KB]: 1023
% 0.21/0.37 % (4138)Time elapsed: 0.003 s
% 0.21/0.37 % (4138)Instructions burned: 4 (million)
% 0.21/0.37 % (4138)------------------------------
% 0.21/0.37 % (4138)------------------------------
% 0.21/0.38 % (4137)Instruction limit reached!
% 0.21/0.38 % (4137)------------------------------
% 0.21/0.38 % (4137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (4137)Termination reason: Unknown
% 0.21/0.38 % (4137)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4137)Memory used [KB]: 5628
% 0.21/0.38 % (4137)Time elapsed: 0.011 s
% 0.21/0.38 % (4137)Instructions burned: 19 (million)
% 0.21/0.38 % (4137)------------------------------
% 0.21/0.38 % (4137)------------------------------
% 0.21/0.38 % (4133)Instruction limit reached!
% 0.21/0.38 % (4133)------------------------------
% 0.21/0.38 % (4133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (4133)Termination reason: Unknown
% 0.21/0.38 % (4133)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4133)Memory used [KB]: 5756
% 0.21/0.38 % (4133)Time elapsed: 0.014 s
% 0.21/0.38 % (4133)Instructions burned: 29 (million)
% 0.21/0.38 % (4133)------------------------------
% 0.21/0.38 % (4133)------------------------------
% 0.21/0.38 % (4141)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (4139)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.38 % (4141)Instruction limit reached!
% 0.21/0.38 % (4141)------------------------------
% 0.21/0.38 % (4141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (4141)Termination reason: Unknown
% 0.21/0.38 % (4141)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (4141)Memory used [KB]: 5500
% 0.21/0.38 % (4141)Time elapsed: 0.003 s
% 0.21/0.38 % (4141)Instructions burned: 5 (million)
% 0.21/0.38 % (4141)------------------------------
% 0.21/0.38 % (4141)------------------------------
% 0.21/0.38 % (4140)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.38 % (4142)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.39 % (4144)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.39 % (4140)Instruction limit reached!
% 0.21/0.39 % (4140)------------------------------
% 0.21/0.39 % (4140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (4140)Termination reason: Unknown
% 0.21/0.39 % (4140)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (4140)Memory used [KB]: 5756
% 0.21/0.39 % (4140)Time elapsed: 0.010 s
% 0.21/0.39 % (4140)Instructions burned: 15 (million)
% 0.21/0.39 % (4140)------------------------------
% 0.21/0.39 % (4140)------------------------------
% 0.21/0.39 % (4143)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (4144)Instruction limit reached!
% 0.21/0.40 % (4144)------------------------------
% 0.21/0.40 % (4144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (4144)Termination reason: Unknown
% 0.21/0.40 % (4144)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (4144)Memory used [KB]: 5628
% 0.21/0.40 % (4144)Time elapsed: 0.009 s
% 0.21/0.40 % (4144)Instructions burned: 16 (million)
% 0.21/0.40 % (4144)------------------------------
% 0.21/0.40 % (4144)------------------------------
% 0.21/0.40 % (4143)Instruction limit reached!
% 0.21/0.40 % (4143)------------------------------
% 0.21/0.40 % (4143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (4143)Termination reason: Unknown
% 0.21/0.40 % (4143)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (4143)Memory used [KB]: 1023
% 0.21/0.40 % (4143)Time elapsed: 0.005 s
% 0.21/0.40 % (4143)Instructions burned: 7 (million)
% 0.21/0.40 % (4143)------------------------------
% 0.21/0.40 % (4143)------------------------------
% 0.21/0.40 % (4139)Instruction limit reached!
% 0.21/0.40 % (4139)------------------------------
% 0.21/0.40 % (4139)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (4139)Termination reason: Unknown
% 0.21/0.40 % (4139)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (4139)Memory used [KB]: 5628
% 0.21/0.40 % (4139)Time elapsed: 0.019 s
% 0.21/0.40 % (4139)Instructions burned: 38 (million)
% 0.21/0.40 % (4139)------------------------------
% 0.21/0.40 % (4139)------------------------------
% 0.21/0.40 % (4145)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (4145)Instruction limit reached!
% 0.21/0.41 % (4145)------------------------------
% 0.21/0.41 % (4145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (4145)Termination reason: Unknown
% 0.21/0.41 % (4145)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (4145)Memory used [KB]: 1023
% 0.21/0.41 % (4145)Time elapsed: 0.003 s
% 0.21/0.41 % (4145)Instructions burned: 3 (million)
% 0.21/0.41 % (4145)------------------------------
% 0.21/0.41 % (4145)------------------------------
% 0.21/0.41 % (4146)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (4146)Instruction limit reached!
% 0.21/0.41 % (4146)------------------------------
% 0.21/0.41 % (4146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (4146)Termination reason: Unknown
% 0.21/0.41 % (4146)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (4146)Memory used [KB]: 1023
% 0.21/0.41 % (4146)Time elapsed: 0.003 s
% 0.21/0.41 % (4146)Instructions burned: 4 (million)
% 0.21/0.41 % (4146)------------------------------
% 0.21/0.41 % (4146)------------------------------
% 0.21/0.41 % (4147)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (4148)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.41 % (4148)Instruction limit reached!
% 0.21/0.41 % (4148)------------------------------
% 0.21/0.41 % (4148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (4148)Termination reason: Unknown
% 0.21/0.41 % (4148)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (4148)Memory used [KB]: 1023
% 0.21/0.41 % (4148)Time elapsed: 0.002 s
% 0.21/0.41 % (4148)Instructions burned: 3 (million)
% 0.21/0.41 % (4148)------------------------------
% 0.21/0.41 % (4148)------------------------------
% 0.21/0.41 % (4147)Instruction limit reached!
% 0.21/0.41 % (4147)------------------------------
% 0.21/0.41 % (4147)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (4147)Termination reason: Unknown
% 0.21/0.41 % (4147)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (4147)Memory used [KB]: 5500
% 0.21/0.41 % (4147)Time elapsed: 0.004 s
% 0.21/0.41 % (4147)Instructions burned: 7 (million)
% 0.21/0.41 % (4147)------------------------------
% 0.21/0.41 % (4147)------------------------------
% 0.21/0.41 % (4149)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.41 % (4149)Instruction limit reached!
% 0.21/0.41 % (4149)------------------------------
% 0.21/0.41 % (4149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (4149)Termination reason: Unknown
% 0.21/0.41 % (4149)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (4149)Memory used [KB]: 5500
% 0.21/0.41 % (4149)Time elapsed: 0.004 s
% 0.21/0.41 % (4149)Instructions burned: 4 (million)
% 0.21/0.41 % (4149)------------------------------
% 0.21/0.41 % (4149)------------------------------
% 0.21/0.42 % (4142)First to succeed.
% 0.21/0.42 % (4151)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.42 % (4150)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.42 % (4152)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.42 % (4142)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.42 % (4142)------------------------------
% 0.21/0.42 % (4142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (4142)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (4142)Memory used [KB]: 5884
% 0.21/0.42 % (4142)Time elapsed: 0.039 s
% 0.21/0.42 % (4142)Instructions burned: 62 (million)
% 0.21/0.42 % (4142)------------------------------
% 0.21/0.42 % (4142)------------------------------
% 0.21/0.42 % (4130)Success in time 0.07 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------